Problem: Multiply the following complex numbers: $({-i}) \cdot ({-5-4i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-i}) \cdot ({-5-4i}) = $ $ ({0} \cdot {-5}) + ({0} \cdot {-4}i) + ({-1}i \cdot {-5}) + ({-1}i \cdot {-4}i) $ Then simplify the terms: $ (0) + (0i) + (5i) + (4 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 5)i + 4i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 5)i - 4 $ The result is simplified: $ (0 - 4) + (5i) = -4+5i $